A popular practice in the industry is to use thermal grease, or grease-like materials, alone or on a carrier to transfer the excess heat across physical interfaces. However, the performance of these materials breaks down or deteriorates when large deviations from surface planarity cause gaps to form between the mating surfaces or when large gaps between mating surfaces are present for other reasons, such as variation in surface heights, manufacturing tolerances, etc. When the heat transfer ability of these materials breaks down, the performance of the component to be cooled is adversely affected. The present invention provides fibrous interfaces that deal effectively with heat transfer across physical interfaces.